Testing Fundamental Physics with Distant Star Clusters: Analysis of Observational Data on Palomar 14

We use the distant outer halo globular cluster Palomar 14 as a test case for classical versus modified Newtonian dynamics (MOND). Previous theoretical calculations have shown that the line-of-sight velocity dispersion predicted by these theories can differ by up to a factor of 3 for such sparse, remote clusters like Pal 14. We determine the line-of-sight velocity dispersion of Palomar 14 by measuring radial velocities of 17 red giant cluster members obtained using the Very Large Telescope and Keck telescope. The systemic velocity of Palomar 14 is (72.28 ± 0.12) km s^(–1). The derived velocity dispersion of (0.38 ± 0.12) km s^(–1) of the 16 definite member stars is in agreement with the theoretical prediction for the classical Newtonian case according to Baumgardt et al. In order to exclude the possibility that a peculiar mass function might have influenced our measurements, we derived the cluster's main-sequence mass function down to 0.53 M⊙ using archival images obtained with the Hubble Space Telescope. We found a mass function slope of α = 1.27 ± 0.44, which is, compared to the canonical mass function, a significantly shallower slope. The derived lower limit on the cluster's mass is higher than the theoretically predicted mass in the case of MOND. Our data are consistent with a central density of ρ_0 = 0.1 M⊙ pc^(–3). We need no dark matter in Palomar 14. If the cluster is on a circular orbit, our spectroscopic and photometric results argue against MOND, unless the cluster experienced significant mass loss.